(a) Suppose that vector w is a linear combination of vectors u1( ( ( ( ( uk and that each u; is a linear combination of vectors v1( ( ( ( ( vm. Prove that w is a linear combination ofv1( ( ( ( ( vm and therefore span (u1( ( ( ( ( uk) ( span (v1( ( ( ( ( vm).
(b) In part (a), suppose in addition that each vj is also a linear combination of u1, . . . , uk. Prove that span (u1( ( ( ( ( uk) = span (v1( ( ( ( ( vm).
(c) Use the result of part (b) to prove that

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